Show that cos(x) - sin (x) can be expressed in terms of a single trigonometric function. Then plot its graph.

Answer 1

Write cosx - sinx = R*cos(x+a)
= R*cosa*cosx - R*sina*sinx

Equating coefficients
Rsina = 1
Rcosa = +1

So tan(a) = 1, thus a = 45 deg or π/4 radians
R = sqrt(2)

cosx - sinx = sqrt(2) * cos(x + 45)

Answer 2

Acos(x) + B sin(x) =
(√(A^2 + B^2))cos(x - tan^-1(B/A))

cos(x) - sin (x) = (√2)cos(x + π/4)

Answer 3

remember that cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
and that cos(pi/4)=sin(pi/4)=sqrt(2)/2
then
cos(x)-sin(x)=sqrt(2)cos(x+pi/4)